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This paper presents a novel non-intrusive sensitivity-based nonlinear finite element model updating method in which the local nonlinearity of structure is considered. The sensitivity analysis is conducted to determine the sensitivity of a dynamic response with respect to different nonlinear parameters using the real and imaginary perturbation method in one single calculation. The use of the imaginary perturbation is capable of second-order accuracy in imaginary perturbation sensitivity analysis of the nonlinear finite element model updating procedure. The nonlinear parameters in the finite element model are estimated by using the improved sensitivity-based optimization algorithm. A nonlinear multi-degree-of-freedom oscillator and a cantilever beam with multiple nonlinear supports are studied to verify the accuracy of the proposed method. The effects of measurement noise and initial parameters on the performance of the presented approach are further investigated. Then, the proposed approach is verified by an experimental test of a cantilever beam with a steel slice. The updated nonlinear finite element model is further evaluated by the structure subjected to new excitations. Results show that the proposed method can effectively update the nonlinear finite element model even in the presence of contaminated measurement data and different initial parameters in the finite element model.

Flight and ground test applications for in-flow and near-wall flow temperature sensing demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-deve...

Optimization of complex structures using standard evolutionary algorithms, like genetic algorithm (GA), is known to be computationally expensive, because a very large number of finite element analy...

Honeycomb sandwich panels are used in aerospace structures for their high stiffness-to-mass ratio. Reducing structural mass is critical in aircraft and spacecraft development due to its direct impa...

Variable angle tow laminates (VAT) and stiffeners are known to redistribute the in-plane load distribution and tailor the buckling mode shapes, respectively, for improving structural performance. To leverage the benefits of using VAT laminates in the practical applications, in the present paper, we discuss buckling load maximization conducted for a stiffened VAT laminated plate with a central cutout considering VAT laminate manufacturing constraints. Three representative boundary conditions as seen in the aerospace structures are considered: in-plane axial displacement, in-plane pure shear, and in-plane pure bending displacements. Two common manufacturing constraints, the one on the automatic fiber placement (AFP) manufacturing head turning radius and the other on the tow gap/overlap, while fabricating VAT laminates are considered in the laminate design. These two manufacturing constraints are modeled by controlling the fiber path radius of curvature and tape parallelism in optimizing the fiber path orientations for the VAT laminates. Stiffener layout and fiber path angle for the VAT laminated plates are both considered in the buckling load maximization study. To avoid using a fine mesh in modeling the stiffened VAT laminates with a cutout when employing the finite element analysis during the optimization, the VAT laminated plate and the stiffeners are modeled independently. The displacement compatibility is enforced at the stiffener–plate interfaces to ensure that the stiffeners move with the plate. Particle swarm optimization is used as the optimization algorithm for the buckling load maximization study. Optimization results show that, without considering AFP manufacturing constraints, the VAT laminates can increase the buckling loads by 21.2% and 12.4%, respectively, comparing to the commonly used quasi-isotropic laminates and traditionally straight fiber path laminates for the structure under the in-plane axial displacement case, 19.7% and 12.5%, respectively, for the in-plane shear displacement case, and 62.1% and 26.6%, respectively, for the in-plane bending displacement case. The AFP manufacturing constraints are found to have different impacts on the buckling responses for the VAT laminates, which cause the maximum buckling load to be 9.3–10.1%, 3.0–3.2%, and 23.2–29.8% less than those obtained without considering AFP manufacturing constraints, respectively, for the present studied model under in-plane axial, shear, and bending displacements. Published version

The paper describes a fully automated process to generate a shell-based finite element model of a large hybrid truck chassis to perform mass optimization considering multiple load cases and multiple constraints. A truck chassis consists of different parts that could be optimized using shape and size optimization. The cross members are represented by beams, and other components of the truck (batteries, engine, fuel tanks, etc.) are represented by appropriate point masses and are attached to the rail using multiple point constraints to create a mathematical model. Medium-fidelity finite element models are developed for front and rear suspensions and they are attached to the chassis using multiple point constraints, hence creating the finite element model of the complete truck. In the optimization problem, a set of five load conditions, each of which corresponds to a road event, is considered, and constraints are imposed on maximum allowable von Mises stress and the first vertical bending frequency. The structure is optimized by implementing the particle swarm optimization algorithm using parallel processing. A mass reduction of about 13.25% with respect to the baseline model is achieved. Published version

Under certain loading conditions, curvilinearly stiffened panels are seen to have better structural performance while being lighter in mass when compared to panels with straight stiffeners. A curvi...

This paper presents results from thermal buckling analysis and optimization of stiffened composite panels with variable angle tow (VAT) laminates and curvilinear stiffeners. Considering the meshing...

Compared to straight fiber path laminates, variable-angle tow (VAT) laminates are known to redistribute the in-plane stress resultants for improving structural buckling response. The VAT laminates ...

With the advances being made in additive manufacturing, it is becoming increasingly possible to fabricate a broad class of complex-shaped designs for practical applications. This manufacturing capa...

Laminated plate structures are analyzed by a discontinuous finite element method with emphasis on determining the transverse shear and normal stress components at the interface of adjacent layers accurately. A Consistent Orthogonal Basis Function Space is used for the interpolation of the displacement field and the traction field between two adjacent layers. The mass matrix of the laminated plate becomes diagonal. Moreover, it is observed that the basis functions are very similar to the vibration mode shapes, even through we do not solve any eigenvalue problem in their generation. These basis functions are uniquely determined by the structure's configuration and associated boundary conditions. The stress field between the layers can be accurately calculated, even for the region near the boundaries that might have sharp stress gradients. Several numerical examples are studied with different boundary conditions. The results for both the deformation and the stress components are compared with the traditional finite element method, especially in terms of the number of degrees-of-freedom (DOF) used in the proposed method and the classic FEM. It is observed that the proposed method is able to use a much fewer number of DOF than that of commercial FEM software (ANSYS etc) to obtain accurate solutions to both the deformation of the plate and the stress field between adjacent layers.

An algorithm that integrates Karhunen-Loeve expansion (KLE), nonlinear finite element method (NFEM), and a sampling technique to quantify the uncertainty is proposed to carry out random vibration a...

This paper presents an efficient finite element approach to study the prestressed vibration mode results of a curvilinearly stiffened composite panel subjected to various in-plane loads. The present method models the plate and the stiffener separately, which allows the stiffener element nodes to not coincide with the plate shell-element nodes. The stiffness and mass matrices of a stiffener are transformed to those of the plate through the displacement compatibility conditions at the plate–stiffener interface via finite element interpolation. Convergence and validation studies have been conducted to verify the present method in the finite element vibration analysis by using the examples from the existing literature. Prestressed vibration mode results are examined for a stiffened composite panel with arbitrarily shaped composite stiffeners in the presence of the in-plane normal and shear loads. Numerical results show the possible benefits of using curvilinear stiffeners to improve the vibration response by ...

An important objective for the aerospace industry is to design robust and fuel efficient aerospace structures. Advanced manufacturing techniques like additive manufacturing have allowed structural designers to make use of curvilinear stiffeners for achieving better designs of stiffened plate and shell structures. Finite Element Analysis (FEA) based standard optimization methods for aircraft panels with arbitrary curvilinear stiffeners are computationally expensive. The main reason for employing many of these standard optimization methods is the ease of their integration with FEA. However, each optimization requires multiple computationally expensive FEA evaluations, making their use impractical at times. To accelerate optimization, the use of Deep Neural Networks (DNNs) is proposed to approximate the FEA buckling response, computed using MSC NASTRAN. The finite element model of a plate is verified with those found in the literature. Later, a Python script is used to generate a large data-set using parallel processing. The 80%, 10% and 10% of the generated data-set are used for training, validation and testing of DNNs, respectively. The results show that DNNs, optimized using Adam optimizer, obtained an accuracy of 95% on the test set for approximating FEA response within 10% of the actual value. To compare the efficiency of the DNN, the trained DNN is used in the optimization of curvilinearly stiffened panels by replacing the conventional FEA. The DNN accelerated the optimization by a factor of nearly 200. The presented work demonstrates the potential of DNN-based machine learning algorithms for accelerating the optimization of curvilinearly stiffened panels.

A stochastic extended finite element method (SXFEM), developed previously by the first two authors, has been extended for the fracture analysis along with reliability analysis of the central cracked laminated composite plate subjected to uni-axial tension with random system properties. The implemented SXFEM approach is based on the M -integral interaction combined with second-order perturbation technique (SOPT) and independent Monte Carlo simulation (MCS) is performed for the evaluation of statistics of mixed mode stress intensity factors (MMSIFs). The random system properties such as material properties, crack length, crack angle, lamination angle, and uni-axial loading, are assumed as input uncorrelated Gaussian random variables. The effect of the different crack angles, crack lengths, lamination angles, and loading on the statistics of MMSIF in terms of mean, standard deviation (SD), probability density function (PDF) and safety factor of cracked laminated composite plate is examined along with the reliability analysis. The effect of crack propagation and its direction along with its effect on the MMSIFs is carried out through global tracking crack growth algorithm. The results obtained by present approach, are compared with an analytical solution and results available in various literature.

The structural optimization of a cantilever aircraft wing with stiffeners and curvilinear spars and ribs is described. The decomposition technique for the wing structure is widely used for the optimization of a complex wing. The optimization procedure is divided into two subsystems: the global wing optimization, which determines the geometry and location of spars and ribs, and local panel optimization to further reduce wing weight. Because the design variables that are changed in the global step have an impact on those changed in the local step and vice versa, an iterative process that iterates between the global and local optimizations is employed. Particle swarm optimization and gradient-based optimization are used to perform integrated global/local optimization. Parallel computing is used, implemented using Python, to reduce the central processing unit time. The license cycle-check method and memory self-adjustment method are developed and applied in the parallel processing framework to optimize the us...

An algorithm that integrates Karhunen–Loeve expansion (KLE) and finite element method (FEM) is proposed to carry out random vibration analysis of complex dynamic systems excited by stationary or non-stationary random processes. In KLE, the auto-covariance function of random process is discretized using orthogonal basis functions. During the response calculations, the eigenvectors of KLE are applied as forcing functions. Three methods are proposed to carry out the random vibration analysis termed as, Method 1A, Method 1B and Method 2. In Method 1A and Method 1B, the basis functions are chosen such that they include multiples of complete or half-cosine and sine functions over the selected time. In Method 2, the basis functions are chosen to be simple piecewise constants. The proposed algorithm is applied to a 2DOF system, a cantilever beam and a stiffened panel for both stationary and non-stationary excitations. Results show that three methods can describe the statistics of the dynamic response with sufficient accuracy. However, Method 1A results have a relatively larger error than that for Method 1B and Method 2 during initial transient time. The Method 2 results have an excellent agreement with analytical results. Moreover, the runtime of Method 2 algorithm is significantly less than both Method 1A and Method 1B algorithms even though its usage results in an increase in the number of KLE terms. Furthermore, Method 2, unlike Method 1A and 1B, neither yields negative and/or infinite eigenvalues for the auto-covariance function nor large inaccuracies.

Motivated by the need for high-fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications, a novel scheme is proposed to accurately compute higher modes of vibration for one-dimensional structures by coupling the classic Ritz method as a predictor and the linear two-point boundary value problem solver SUPORE as a corrector. The Ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes. These estimates are then used as initial guesses by SUPORE, which employs superposition and reorthonormalization to accurately solve the governing boundary value problem. Compared to a high-fidelity Ritz approximation or a highly refined finite element modeling procedure, this is a simple, computationally less expensive, and yet highly accurate method to compute mode shapes for applications that require higher modes. This scheme is used to compute mode shapes within an absolute and relative...

We investigated the natural frequencies and mode shapes of a freely vibrating, integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners as opposed to the normally employed rib stiffeners. Both the plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a tensor product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used in this paper can also be applied to fully clamped, free, and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh–Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loo...

This paper finds up to lowest 100 free vibration frequencies of isotropic and linearly elastic plates with thickness to side length ratio varying from 0.001 to 0.5 by using the Ritz method, a third-order shear and normal deformable plate theory (TSNDT), and weighted Jacobi polynomials as admissible functions that are mutually orthogonal and exactly satisfy essential boundary conditions. The numerical method is stable even for 18th degree polynomials as basis functions. It is shown that this approach requires fewer degrees of freedom than those in the traditional finite element method (FEM) to find converged lowest 100 frequencies and the corresponding mode shapes. No shear correction factor is employed in the TSNDT. The presently computed results agree well with those from either analytical or numerical solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial FE software, Abaqus. Furthermore, results for plates made of an incompressible material can be computed by setting Poisson's ratio = 0.49.

This research presents the Non-Uniform Rational B-Splines (NURBS) based isogeometric finite element analysis of stiffened laminated composite plates. A first-order shear deformation theory is used to derive the governing equations by employing a variational formulation. Isotropic, orthotropic and laminated composite plates stiffened with multiple curvilinear stiffeners of different profiles are investigated. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load due to the presence of circular and elliptical cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency of the proposed formulation when compared to other published solutions and those obtained using ABAQUS, a commercial software.

This paper presents a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using the Ritz method by employing classical orthogonal Jacobi polynomials. Both the plate and stiffeners are modeled using first-order shear deformation theory (FSDT). The displacement and rotations of the plate and stiffeners are approximated by separate sets of Jacobi polynomials. The ease of modification of the Jacobi polynomials enables the Jacobi weight function to satisfy geometric boundary conditions without loss of orthogonality. The distinctive advantage of Jacobi polynomials, over other polynomial-based trial functions, lies in that their use eliminates the well-known ill-conditioning issues when a high number of terms are used in the Ritz method, e.g., to obtain higher modes required for vibro-acoustic analysis. In this paper, numerous case studies are undertaken by considering various sets of boundary conditions. The results are verified both with the detailed finite element analysis (FEA) using commercial software msc.nastran and with those available in the open literature. New formulation and results include: (i) exact boundary condition enforcement through Jacobi weight function for FSDT, (ii) formulation of quadrilateral plates with curvilinear stiffeners, and (iii) use of higher order Gauss quadrature scheme for required integral evaluations to obtain higher modes. It is demonstrated that the presented method provides good numerical stability and highly accurate results. The given new numerical results and convergence studies may serve as benchmark solutions for validating the new computational techniques.

An optimization framework is developed to minimize structural weight of the front-frame of heavy-duty trucks while satisfying stress constraint. The shape of the frame is defined by a number of design parameters (which define the shape of the side-rail, position and width of the internal brackets, and width of the flanges). In addition, the thickness of the engine-mount, the side-rails, inner-brackets, radiator mount, shock absorber and cab-mount connector are also considered as design variables. Aluminum Alloy, 6013-T6 is chosen as the material and the maximum allowable stress is the yield stress (320 MPa). A quantity known as ‘Violation’ is defined as the ratio of area in the front-end module where stress constraint is violated to the total area of the frame is introduced to implement stress constraints. For optimization, the penalty method is used where the objective is to minimize the total weight while keeping the value of the ‘Violation’ parameter less than 0.1 %. The Particle Swarm Optimization Algorithm is implemented using parallel computation for optimizing the structure. Commercial FEA software MSC.PATRAN is used for creating the geometry and the mesh whereas MSC.NASTRAN is used to perform static analysis. Six design load conditions, each corresponding to a road condition are used for the problem.

Innovative manufacturing technology has led to the fabrication of complex shape and multi-functional structures by using the concept of integrated and bonded unitized structural components. To study the stability behavior of such structural designs, this paper presents an efficient finite element buckling analysis of unitized stiffened composite panel stiffened by arbitrarily shaped stiffeners. A first-order shear-deformation theory is employed for both the panel and the stiffeners. Displacement compatibility conditions are imposed at the panel-stiffeners interfaces. To obviate remeshing when the stiffener shape changes, the stiffeners’ geometry and displacement are expressed in terms of those of the panel middle surface through compatibility conditions that make use of the interpolation polynomials employed in the finite element method. To accommodate any shaped stiffeners, a generalized geometry parametrization tool is developed to parameterize the shape of the stiffeners including the stiffener placement and the stiffener geometric curvature. Convergence and validation studies using the present method for the buckling analysis of stiffened isotropic and composite panels are conducted to illustrate the accuracy of the present method. Parametric studies show that the stiffener placement, the stiffener geometric curvature, the stiffener depth ratio (height-to-width ratio) and laminates fiber ply orientation influence both the plate bucking load and the correspond buckling mode shape. The tailoriability of the stiffeners shape and the laminates fiber ply orientation provides an enhanced design space in the structural design for improving the structural stability.

The constitutive behavior of a continuum equivalent to cellular core are calculated using detailed finite element models of representative unit cell for hexagonal, square and triangular core shapes. The variation of the constitutive behavior of the homogeneous structure equivalent to the cellular core with respect to the core density is studied. Formulas for direct calculation of the constitutive behavior are generated for cell size range 1/8″ to 3/8″ and core density range 1.0 pcf to 8.1 pcf. The calculated properties are tested using two-dimensional and three-dimensional finite element modeling techniques of sandwich panels. Error analysis is then performed to identify the effect of the panel size to cell size ratio as well as the facesheet thickness to core thickness ratio on the error. Results show linear variation of mechanical properties with core density except for panel-wise in-plane shear modulus which is too low and can be neglected. The facesheet thickness to core thickness ratio was found to have low impact on the error while the panel size to cell size ratio was found to have a significant impact on the error level. A minimum panel size to cell size ratio of 60 was found to be necessary to maintain error within 5%.

A finite element method based approach is developed for studying the static, vibration, and buckling behaviors of curvilinearly stiffened plates in the presence of in-plane compressive and tensile stresses. The first-order shear deformation theory is employed for both the plate and the Timoshenko beam modeling. Interpolation functions are used to build the displacement mapping between the stiffener and the plate nodes to allow the stiffener to be placed anywhere within the plate. One of the advantages of the present method is that the plate need not be remeshed while the stiffener configuration is changed; another advantage is that the results obtained by the present method with a much fewer number of elements match well with the results obtained by using a commercial finite element method software. Several numerical examples are solved to study both the static and dynamic behaviors of stiffened plates. The effects of boundary conditions, stiffener eccentricity, stiffener curvature, stiffener-plate geomet...

Experimental vibration testing is a common technique employed to identify modal frequencies, mode shapes, and at times, modal damping. The identified data can then be used for updating the structural dynamic models, e.g. those obtained by using approaches like the finite element method. It can also be used to identify any damage in the structure. For many symmetric structures like buildings, large shells such as cooling towers, bridges, and aircraft, conventional flexible modes are often separated into symmetric and anti-symmetric modes. This leads to significant reduction in computing both the natural modes and frequencies, and the resulting dynamic responses. However, in practice, during fabrication and manufacturing of these structures, or due to damage during their operation, it is often observed that the structure can develop significant asymmetry. As a result, for real structures, the often assumed separation into symmetric and antisymmetric modes no longer holds. The modes start to possess both symmetric and antisymmetric components in the same mode, which then poses a significant challenge for both modal identification and FEM modeling. Furthermore, it can significantly change the dynamic response of structures. This paper describes the process of ground vibration test, modal identification and FEM modeling for an asymmetrical aircraft. Details of the best practices for incorporating the asymmetry during the model updating process is discussed and the results of the GVT and FEM updating procedure for the aircraft are described. The FEM update procedure successfully identifies the source of the asymmetry. The suitability of the FEM update procedure for characterizing the source of asymmetry is discussed.

With improvement in innovative manufacturing technologies, e.g. automated tow-placement, it is now possible to fabricate any complex shaped structural design for practical applications. This innovative manufacturing technology allows for the fabrication of curvilinearly stiffened pressure vessels and pipes. Compared to straight stiffeners, curvilinear stiffeners have been shown to have better structural performance and weight savings under certain loading conditions. In this paper, an optimization framework for optimal structural design for curvi-linearly stiffened composite pressure vessels and pipes is presented. Non-Uniform Rational B-Spline (NURBS) curves are utilized to define curvilinear stiffeners over the surface of the pipe. An integrated tool using Python, NURBS-based Rhinoceros 3D, MSC.PATRAN and MSC.NASTRAN is implemented for performing topology optimization of curvilinearly stiffened cylindrical shells. Rhinoceros 3D is used for creating the geometry, which later can be exported to MSC.PATRAN for finite element model generation. Finally, MSC.NASTRAN is used to perform structural analysis. A hybrid optimization technique, consisting of Particle Swarm Optimization (PSO) and Gradient Based Optimization (GBO), is used for finding the optimized locations of stiffeners, optimal geometric dimensions for stiffener cross-sections and the optimal layer thickness for the composite skin. Optimization studies show that stiffener placement influences the buckling mode of the structure. Furthermore, the structural weight can be decreased by optimizing the stiffener’s cross-section and skin thickness. In this paper, a cylindrical pipe stiffened by orthogonal and curvilinear stiffeners under internal pressure and bending load is studied. It is shown that curvilinear stiffeners lead to a potential 8% weight saving in the composite laminated skin as compared to the case of using straight stiffeners.

A multi-objective vibro-acoustic design optimization of straight or curvilinearly stiffened panels excited by an acoustic diffuse field is performed. During design optimization, the panel mass and the radiated acoustic power are the two objectives to be minimized while satisfying constraints on buckling, von Mises stress and crippling. Based on the concept of plane wave propagation, a diffuse acoustic field is developed for use along with a finite element model. To represent the panel's structural behavior, the dynamic analysis of the panel is performed for the developed diffuse acoustic excitation and the radiated acoustic power is calculated using the velocities obtained from the dynamic analysis. A baseline design is obtained by optimization study with mass as an objective to be minimized while constraints are put on buckling, von Mises stress and crippling. The obtained baseline grid stiffened panel is used for a comparative study of a panel with curvilinear stiffeners in vibro-acoustics with diffuse sound field as the source of the excitation.

Laminated composites are becoming very popular in the aerospace industry because of their high strength-to-weight ratio and the fact that their properties can be tailored by changing different parameters like fiber and matrix materials, ratio of fiber to matrix volumes, fiber orientations, sequence of the plies, etc. However, because of their heterogeneity, an accurate analysis of composite laminates requires very high time and storage space. In the presence of structural discontinuities like cracks, delaminations, cutouts, etc., the computational complexity increases significantly. A possible alternative to reduce the computational complexity is the global–local analysis, which involves an approximate analysis of the whole structure followed by a detailed analysis of a significantly smaller region of interest. We investigate here the performance of the global–local scheme based on the finite-element method by comparing it to the traditional finite-element method. To do so, we conduct a two-dimensional st...

A parameterization of the aircraft shape is needed for a correct mathematical definition of the structure and its components. The parameterization allows the definition of the geometry as a function of a few meaningful parameters. Traditionally, the aircraft industry focused on developing a universal parameterization of the aircraft outer mold line to facilitate the automatic construction of complex aerodynamic meshes to be used in computational fluid dynamics calculations and aerodynamic shape optimization problems. More recently, the attention of researchers has shifted toward the internal structure topology parameterization. The introduction of new design concepts such as SpaRibs (spars and ribs) requires the capability to define the geometric shape of the internal wing components for a correct automatic generation of the finite element mesh. The aim of this research is to present a simple and efficient way to parameterize the topology of the internal structure of complex wings. Spline curves are used ...

The feasibility of harvesting energy using polyvinylidene fluoride patches mounted on a vibrating prestressed membrane, itself attached to a tensegrity structure, was investigated. Kinematics of the tensegrity structure and the attached membrane is described and conditions for stable equilibrium for the structure are derived. Nonlinear partial differential equations describing the dynamics of the membrane attached to the tensegrity structure and under the action of a time-dependent transverse pressure are derived using the principle of virtual work. These equations are linearized and the modes of the structure are obtained using the finite element method. These modes are used as basis functions in developing a reduced-order model to obtain the response of the complete structure under the applied transverse dynamic pressure. The polyvinylidene fluoride patch on the structure is connected to an electrical load resistance. The electrical current passing through the load resistance is calculated using Gauss’s...

The integrated local Petrov–Galerkin sinc method was used with an irreversible exponential traction-separation constitutive law for modeling mode I and mixed-mode delamination of an adhesively bonded aluminum and hybrid plane-strain and plane-stress structural specimen. The first-order shear deformable theory was used to model the specimen both above and below the delamination with the sublaminate interfaces coupled to each other through the cohesive zone model. Through-the-sublaminate-thickness distributions of interlaminar stresses were obtained using integration of the equilibrium equations of three-dimensional elasticity. An adaptive discretization technique is developed and implemented. Because the sinc points, distributed by the double exponential transformation, are biased toward the boundary in the integrated local Petrov–Galerkin sinc method, the adaptive sinc point distribution allows an accurate solution to be obtained with far fewer sinc points than when a single subdomain is used. The results...

This article studies finite element model updating of a composite flying-wing aircraft by using experimental results for both the aircraft and its components obtained in different experimental setups. A multi-level optimization approach is employed for updating the finite element models for obtaining the analysis results to match with the test results for both the global model and its components. The mass and stiffness distributions are, respectively, updated in the multi-level optimization problems. The first level optimization (Level I) updates the mass distribution, while keeping the stiffness distribution fixed. The optimal mass distribution obtained in Level I passes and are fixed in the second level optimization (Level II) for updating the stiffness related parameters. The back-and-forth iteration between these two levels continues till a convergence criteria is achieved. Both the root mean square error (RMSE) and the mean absolute error (MAE) are used as fitness functions in the optimization problems. Recognizing the nonsmooth nature of the MAE in the design domain, the optimization problem using the MAE as the fitness function is converted to a sequential linear programming problem by treating each absolute difference value as a design variable. Optimization results show that when using the MAE based optimization, some of the analysis results for the updated FEM are exactly same as the test data while RMSE based optimization distributes the errors to all responses. The multi-level optimization splits the large cost function as used in the all-at-once (AAO) optimization into two small cost functions and achieves a slightly lower fitness function than that for the AAO optimization when they have the same convergence criteria. As a result, the responses for the updated models obtained from the multi-level optimization are closer to the test results.

Accurately capturing the stress distribution in an adhesive joint of aircraft structures requires discretizing the adhesive layer with a very fine finite element mesh. Because such a simulation requires high computational processing unit time, researchers are looking for alternative methods to simulate adhesive joints of aircraft structures for saving the computational processing unit time. Another high computational processing unit requiring the study of aircraft structures is the evaluation of delamination growth in adhesive joints and crack propagation in brittle materials using cohesive zone modeling along with the very fine finite element mesh for the bulk material. To reduce these computational times, a possible alternative is to use a global–local finite element method. Therefore, both the crack propagation and the characteristics of adhesive joints were studied using a global–local finite element method. Three cases were studied using the proposed global–local finite element method, including 1) a...

This research paper describes the development of NURBS Isogeometric finite element analysis and post-processor for interlaminar stress calculation in composite and sandwich plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Linear, quadratic, higher order and k -refined NURBS elements are constructed and numerical validation is performed for laminated composite and sandwich plates. Lagrange finite element suffers from higher order stress gradient oscillations due to Gibbs phenomenon and require alternative stress recovery procedures for accurate interlaminar stress calculations, especially interlaminar normal stress. In this paper, direct post-processing is performed which computes interlaminar shear and normal stresses from higher order gradients of NURBS basis in a single step procedure. Interlaminar stresses are found to be in an excellent agreement with 3D elasticity solution and FSDT along with k -refinement procedure of NURBS basis is found to compute equivalent or better interlaminar normal stress than higher-order shear deformation theory.

A neurofuzzy system has been proposed to detect damage in a structure with multiple damage sites. A prestressed square membrane representing a gossamer structure has been taken as the example structure. Damage at various locations on the structure has been modeled as reduced stiffness. The structure undergoes transverse vibration under the action of a transverse dynamic pressure. Using the finite element package, “ABAQUS,” the strain histories at different sensor locations in the structure under the action of the transverse dynamic pressure were calculated. The vibration response of the structure has been decomposed into a set of subsignals using wavelet analysis to define a damage feature index vector, which has been used as an indicator of damage in the membrane. The neurofuzzy system accepts the wavelet-based damage feature index vector as the input and gives the damage status of the structure as the output.

A global–local finite element analysis was performed to study the damage tolerance of curvilinearly stiffened panels, fabricated using the modern additive-manufacturing process that can create so-called unitized structures. In the first step, a buckling analysis of panels was performed to determine whether the panels satisfied the buckling constraint in an undamaged state. In the second step, stress distributions in the panel were analyzed to determine the location of the critical stress under combined shear and compression loadings. Then, a fracture analysis of the curvilinearly stiffened panel with a crack designed at the earlier-obtained location of the critical stress, which was the common location with the maximum magnitude of the principal stresses and von Mises stress, was performed under combined shear and tensile loadings. A mesh-sensitivity analysis was performed to validate the choice of the mesh density near the crack tip. All analyses were performed using the global–local finite element metho...

Future aerospace vehicles like hybrid wing/body, truss-braced wing, and “double bubble” would have pressurized noncircular fuselage structures and complex wing geometry. Traditional aircraft designs have led to the confidence and experience of designing such structures using the knowledge base built over the years and the resulting rules of thumb. However, there is a lack of experience of load calculations and design of complex, multifunctional, aircraft structural concepts for future aerospace vehicles. Designing such structures will require a physics-based optimization framework. Therefore, a new optimization framework, EBF3PanelOpt, is being developed. Commercial software MD-PATRAN (geometry modeling and mesh generation) and MD-NASTRAN (finite-element analysis) are integrated in EBF3PanelOpt framework using the Python programming environment to design stiffened panels with curvilinear stiffeners. Currently, EBF3PanelOpt optimizes the stiffened panel with curvilinear blade stiffeners, where the loads ar...

The objective of the current paper is to present a Ritz-type solution for the buckling analysis of cracked-orthogonally stiffened panels. A cracked-orthogonally stiffened panel is defined as a rectangular plate with a crack and that has stiffeners that are parallel to one of its sides. Such structures are typically used as stiffened wing skins and fuselage skins in aerospace engineering. The behavior prediction of a cracked-stiffened panel using the Ritz approach is considered in the paper. In the Ritz-type solution, we use the local trigonometric trial functions to define the displacement function of the crack-stiffened panel, which is discretized into several elements based on the crack location and stiffener location. The interface continuity conditions for cracked thin-walled structures are derived and investigated in detail; the interface conditions are used to condense the global eigenvalue problem by eliminating redundant Ritz coefficients. Examples are presented to illustrate the effectiveness of ...

A new framework, EBF3PanelOpt, is being developed for design and optimization of complex, multifunctional, aircraft structural concepts like pressurized non-circular fuselage structures to be used in hybrid wing/body vehicles that are subjected to complex structural loading cases. This tool can be used to integrate materials and structural concepts to exploit emerging additive manufacturing processes that offer the ability to efficiently fabricate complex structural configurations. Commercial software packages, MD-Patran (geometry modeling and mesh generation), MD-Nastran (Finite Element Analysis), are integrated in the EBF3PanelOpt framework using Python programming environment to design stiffened panels with curvilinear stiffeners. Typically, these panels experience multiple loading conditions during the operations of these vehicles. EBF3PanelOpt has the capability to optimize flat/curved multi-sided panels with straight/curved edges having curvilinear, blade-type stiffeners under multiple loading conditions. The mass of the panel is minimized subjected to constraints on buckling, von Mises stress, and crippling or local failure of the stiffener using global optimization techniques or gradient based optimization techniques. The panel/stiffener geometry is parametrized using design variables that include variables for orientation and shape of the stiffeners, the thicknesses and height of the stiffeners, and the plate thickness. The plate can have uniform thickness or non-uniform thicknesses for the pockets created by the stiffeners. During optimization, constraints can be applied for each of the loading conditions by aggregating all the responses using Kreisselmeir–Steinhauser criteria or using worst response amongst all the responses or applying all the constraints. Initially, the flat rectangular panel is optimized for the single load-case to study the effectiveness of the panel thickness option. Then, the optimization of flat rectangular and cylindrical panels is carried out for three sample load cases of practical interest. This paper discusses the advantages and disadvantages of the proposed constraints' application.

The SpaRibs topology of an aircraft wing has a significant effect on its structural behavior and stability as well as the flutter performance. The development of additive manufacturing techniques like Electron Beam Free Form Fabrication (EBF3) has made it feasible to manufacture aircraft wings with curvilinear spars, ribs (SpaRibs) and stiffeners. In this article a new global-local optimization framework for wing with multiple sections using curvilinear SpaRibs is described. A single design space is used to parameterize the SpaRibs geometry. This method has been implemented using MSC-PATRAN to create a broad range of SpaRibs topologies using limited number of parameters. It ensures C0 and C1 continuities in SpaRibs geometry at the junction of two wing sections with airfoil thickness gradient discontinuity as well as mesh continuity between all structural components. This method is advantageous in complex multi-disciplinary optimization due to its potential to reduce the number of design variables. For the global-local optimization the local panels are generated by an algorithm which is totally based on a set algebra on the connectivity matrix data. The great advantage of this method is that it is completely independent of the coordinates of the nodes of the finite element model. It is also independent of the order in which the elements are distributed in the FEM. The code is verified by optimizing of the CRM Baseline model at trim condition at Mach number equal to 0.85 for five different angle of attack (-2deg, 0deg,2deg,4deg and 6deg). The final weight of the wing is 19,090.61 lb. This value is comparable to that obtained by Qiang et al. 6 (19,269 lb).

This research present the development of geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Geometric nonlinearity is accounted for in Von-Karman sense. A family of NURBS elements are constructed from refinement processes and validated using various examples. k -refined NURBS elements are developed to study thin plates. Isotropic, orthotropic and laminated composite plates are studied for various boundary conditions, length to thickness ratios and ply-angles. Computed center deflection is found to be in an excellent agreement with the literature. For thin plate analysis, linear and k -refined quadratic NURBS element is found to remedy the shear locking problem. k -refined quadratic NURBS element provide stabilized response to distorted, coarse meshes without increasing the order of the polynomial, owing to the increased smoothness of solution space.

The present work addresses the structural-acoustic design optimization study of straight or curvilinearly stiffened panels excited by turbulent boundary layer (TBL) pressure fluctuation. The Corcos model of representing TBL is used to capture the correlation of TBL pressure excitation. Validation of the Corcos TBL model, implemented in a framework, named EBF3PanelOpt, is also performed. For a comparative study, two optimal baseline designs are obtained for a panel with two and four stiffeners, respectively. The optimal designs obtained by performing acoustic optimization have reduced the maximummean square pressure radiated in the far field by 11.4 dB for a panel with two stiffeners and 18.5 dB for a panel with four stiffeners. The reduction of mass and the acoustic response during structural-acoustic optimization are conflicting in nature. Therefore, amulti-objective design optimization using the nondominated sorting genetic algorithm-II (NSGA-II) in VisualDoc is performed. The best Pareto-optimal design with four stiffeners, obtained using the multi-objective design optimization approach, has reduced the maximum mean square pressure radiated in the far field by 4.8 dBwhen comparedwith the baseline designwith four stiffeners. The obtained optimal designs meet all of the constraints, such as buckling eigenvalue, von Mises, and crippling stresses.

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.